1/x+x-1=x+2x=

Solution for 1/x+x-1=x+2x= equation:

1/x+x-1=x+2x=

We move all terms to the left:

1/x+x-1-(x+2x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

1/x+x-(+3x)-1=0

We add all the numbers together, and all the variables

x+1/x-(+3x)-1=0

We get rid of parentheses

x+1/x-3x-1=0

We multiply all the terms by the denominator


x*x-3x*x-1*x+1=0

We add all the numbers together, and all the variables

-1x+x*x-3x*x+1=0

Wy multiply elements

x^2-3x^2-1x+1=0

We add all the numbers together, and all the variables

-2x^2-1x+1=0

a = -2; b = -1; c = +1;
Δ = b2-4ac
Δ = -12-4·(-2)·1
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-2}=\frac{4}{-4}
=-1
$